They may not agree on much, but China, Japan, South Korea and the United States appear to share one common interest – to prevent North Korea’s nuclear weapons from destabilizing Asia.

Yet as U.S. Secretary of State John Kerry makes a three-nation swing through Asia this week, the fissures that divide these countries are complicating the task of pressuring North Korea to abandon its nuclear ambitions.

At a press conference late Friday in Beijing, Kerry said he had productive conversations with top Chinese leaders, who he said “could not have been more emphatic” in their desire to stop North Korea’s nuclear program “over the long run.”

But Kerry also acknowledged that he and President Barack Obama have major differences with China on human rights and China’s recent claims on vast ocean expanses off its coasts. So the question becomes whether Obama and Kerry will risk expending their political capital on those issues at the possible expense of a major foreign policy prize – a less dangerous North Korea.

Kerry spent Friday meeting with Chinese President Xi Jinping and other top Chinese officials. He said that he and his Chinese hosts discussed specific steps that could be undertaken to prod North Korea into what diplomats called “denuclearization.” Kerry wouldn’t say what those steps are, but he said that both sides are taking their separate proposals “under advisement” to be subjects for further discussion.

China has had longstanding concerns about North Korea’s bellicose and unpredictable behavior, highlighted recently when North Korean leader Kim Jong Un purged and executed his uncle, Jang Song Thaek, who was close to Beijing.

Even so, few foreign analysts think China will apply heavy pressure to persuade Kim to re-engage in six-party talks that seek to prompt North Korea to give up its nuclear program in return for aid. Such talks haven’t been held since 2008. For now, Beijing appears to be figuring its relationship with Kim in light of his execution of his uncle.

On Thursday, Kerry spent time with top government officials in South Korea, after which he made clear that North Korea’s nuclear program would be a major focus of his two days in Beijing.

“No country has a greater potential to influence North Korea’s behavior than China, given their extensive trading relationship with the North,” Kerry told reporters in Seoul. As Kerry noted, North Korea depends on China for fuel, banking and hard currency through trade.

If Beijing is to play the role Kerry wants, it surely will ask the United States for reciprocity on its priorities. These include reduced military aid to Taiwan and a settling of territorial claims that have triggered recent feuds between China and Japan, Vietnam and the Philippines.

To complicate matters further, U.S. ally South Korea has its own territorial disputes with U.S. ally Japan, over a set of islands known as the Dokdo by South Koreans and Takeshima by the Japanese. Both South Korea and China have long memories about Japanese atrocities during World War II, which were rekindled when Japanese Prime Minister Shinzo Abe recently visited a war shrine that honors known war criminals.

Part of Kerry’s visit is designed to send the message that the Obama administration still wants to “rebalance” U.S. foreign policy to focus more on China and Asia. This is Kerry’s fifth trip to Asia, and his second to China since becoming secretary of state last year. He travels to Indonesia on Saturday. This week, the White House announced that Obama will visit Japan, South Korea, Malaysia and the Philippines in April.

Despite those travels, numerous Asia watchers complain that administration focuses far too much on the Middle East. Obama barely mentioned Asia in his State of the Union address. Yet other analysts criticize the administration for another reason – using “rebalance” as a pretext for escalating military involvement in Asia.

In a recent commentary in the China Daily, Stephen Harner, an Asia consultant and former State Department official, said the United States risks triggering a regional arms race with its aggressive stance toward China.

“The U.S. ‘rebalance’ to Asia policy looks more than anything like a Department of Defense strategy to keep and grow Pentagon personnel levels, budgets and new weapons development, under the pretext of ‘strengthening alliances,’” Harner wrote.

In his Beijing news conference, Kerry stressed the potential for China and the United States – “the two most powerful economies of the world” – to achieve major accomplishments by focusing on areas of mutual agreement and working respectfully on issues where both sides disagree.

“China and the United States are cooperating on big-ticket items,” said Kerry, adding that joint efforts by both countries to address climate change, clean energy and conflicts in Iran and Afghanistan have gotten less attention than they deserve.